6. Twenty percent of all trucks undergoing a certain inspection will fail the inspection. Assume that trucks are independently undergoing this inspection, and that they are inspected one at a time. A researcher is interested in the number of trucks that are inspected until one fails inspection.

a. Explain why this satisfies a geometric setting. (Remember there are 4 conditions to check)

b. Find the expected number of trucks that must be inspected until a truck fails inspection for the first time. Show your work.

c. What is the probability that the 5 th truck inspected is the first truck to fail inspection? Show your work.

d. What is the probability that it takes more than 3 trucks until the 1st truck fails inspection (i.e. the first truck to fail inspection happens after the 3 rd truck inspected)? Show your work.